Question: Solve for $k$, $ \dfrac{5k - 9}{5k + 4} = \dfrac{1}{9} $
Solution: Multiply both sides of the equation by $5k + 4$ $ 5k - 9 = \dfrac{5k + 4}{9} $ Multiply both sides of the equation by $9$ $ 9(5k - 9) = 5k + 4 $ $45k - 81 = 5k + 4$ $40k - 81 = 4$ $40k = 85$ $k = \dfrac{85}{40}$ Simplify. $k = \dfrac{17}{8}$